Theorems · Theorem · commutative algebra
MvPolynomial.coeff_eq_zero_of_totalDegree_lt
∀ {R : Type u} {σ : Type u_1} [inst : CommSemiring R] {f : MvPolynomial σ R} {d : σ →₀ ℕ},
f.totalDegree < ∑ i ∈ d.support, d i → MvPolynomial.coeff d f = 0- Defined in
- Mathlib.Algebra.MvPolynomial.Degrees
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 62 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommSemiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- CommSemiringstatement and proof · cited by 10,911
- Finsuppstatement and proof · cited by 5,255
- Finset.sumstatement and proof · cited by 5,195
- MvPolynomialstatement and proof · cited by 2,140
- Finsupp.supportstatement and proof · cited by 828
- Finset.supproof · cited by 530
- Finsupp.sumproof · cited by 481
- lt_of_le_of_ltproof · cited by 432
- MvPolynomial.coeffstatement · cited by 315
- MvPolynomial.supportproof · cited by 220
- lt_irreflproof · cited by 190
Cited by3
Results whose statement or proof uses this declaration.
- MvPolynomial.totalDegree_eq_zero_iff_eq_Cproof · cited by 9
- MvPolynomial.sum_homogeneousComponentproof · cited by 0
- MvPolynomial.combinatorial_nullstellensatz_exists_eval_nonzeroproof · cited by 0